THEOREM OF THE DAY: Torricelli’s Trumpet

Theorem

Suppose that the hyperbola  $y=\dfrac{1}{x}$  is rotated about the x axis, in the interval $[1, ∞)$, through one complete turn (τ radians) to form a solid, and to this is added a cylinder of radius and height 1. Then the combined volume is equal to that of a cylinder of height 1 and radius $\sqrt{2}$.

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